2-1	THE NATURE OF DATA
Information you gather is called data. Data can be a factual statement of physical phenomena. For example, the statement "the copper was removed by the chemical reaction with ferric chloride" is descriptive data. When data is purely descriptive, it is said to be qualitative data. When a quantity is measured, we associate numerical values with it, and the information is more useful in a scientific way because more information is present. Information about the magnitude or intensity of a physical phenomenon is called quantitative data. Recall that the quantity that is being measured is called the measurand. Instrumentation extends the human senses by allowing a numerical value or values to be associated with the measurand.
      Numerical data can be categorized in several ways. It can be an isolated value or can be dependent on time or location. Values recorded directly from an experiment or observation are called empirical data. Prior to processing, empirical data is often referred to as raw, or unprocessed, data, whereas data that has been analyzed is called processed data. Data can also be generated by theoretical calculations. Frequently, theoretical data is compared to measured or processed data as a test of the theoretical model.
      After data is collected, it may need to be processed either by applying mathematical computations to it or by arranging it in some meaningful manner. This procedure is called data processing or data reduction. Data may be entered into a computer for reduction, or, in some cases, the measurement instrument may perform the data reduction within the instrument. For example, a digital oscilloscope may present the rms value of a voltage as a displayed numeric value. As part of the process of data reduction, obvious errors or discrepancies should be looked for; sometimes statistical processing is applied to indicate the nature of experimental precision.
      After the data is reduced, it is analyzed. Data analysis is the process of trying to make results from a measurement meaningful and to resolve any differences due to variations in the data. The data-analysis step should consider the consistency  of the data, experimental errors and limitations, approximations in the data-reduction process, and other factors that could affect the interpretation of the data. The combination of these effects is used to support a conclusion. After analysis, the data serves as the basis of a report.
2-2	ERROR, ACCURACY, AND PRECISION
Data measured with test equipment is not perfect; rather, the accuracy of the data depends on the accuracy of the test equipment and the conditions under which the measurement was made. In order to interpret data from an experiment, we need to have an understanding of the nature of errors. Experimental error should not be thought of as a mistake. All measurements that do not involve counting are approximations of the true value. Error is the difference between the true or best accepted value of some quantity and the measured value. A measurement is said to be accurate if the error is small-accuracy refers to a comparison of the measured and accepted, or "true," value. It is important for the user of an instrument to know what confidence can be placed in it. Instrument manufacturers generally quote accuracy specifications in their literature, but the user needs to be cautioned to understand the specific conditions for which an accuracy figure is stated. The number of digits used to describe a measured quantity is not always representative of the true accuracy of the measurement.
    Two other terms associated with the quality of a measurement are precision and resolution. Precision is a measure of the repeatability of a series of data points taken in the measurement of some quantity. The precision of an instrument depends  on both its resolution and its stability. Recall that resolution was defined in Section 1-1 as the minimum discernible change in the measurand that can be detected. Stability refers to freedom from random variations in the result. A precise measurement requires both stability and high resolution. Precision is a measure of the dispersion of a set of data, not a measure of the accuracy of the data. It is possible to have a precision instrument that provides readings that are not scattered but that are not accurate because of a systematic error. However, it is not possible to have an accurate instrument unless it is also precise.
    The resolution of a measurement is not a constant for a given instrument but may be changed by the measurand or the test conditions. For example, a nonlinear meter scale has a higher resolution at one end than at the other due to the spacing of the scale divisions. Likewise, noise induced in a system can affect the ability to resolve a very small change in voltage or resistance. Temperature changes can also affect measurements because of the effect on resistance, capacitance, dimensions of mechanical parts, drift, and so forth.
SIGNIFICANT DIGITS
When a measurement contains approximate numbers, the digits known to be correct are called significant digits. The number of significant digits in a measurement depends on the precision of the measurement. Many measuring instruments provide more digits than are significant, leaving it to the user to determine what is significant. In some cases, this is done because the instrument has more than one range and displays the maximum number of significant digits on the highest range. If the instrument is set to a lower range, the instrument may show the same number of digits despite the fact that the rightmost digits are not significant. This
can occur when the resolution of the instrument does not change as the range is changed. The user needs to be aware of the resolution of an instrument to be able to determine correctly the number of significant digits.
      When reporting a measured value. the least significant uncertain digit may be retained, but other uncertain digits should be discarded. To find the number of significant digits in a number, ignore the decimal place and count the number of digits from left to right, starting with the first nonzero digit and ending with the last digit to the right. All digits counted are significant except zeros to the right end of the number. A zero on the right end of a number is significant if it is to the right of the decimal place; otherwise it is uncertain. For example. 43.00 contains four significant digits. but the whole number 4300 may contain two. three, or four significant digits. In the absence of other information, the significance of the right-hand zeros is uncertain. To avoid confusion, a number should be reported using scientific notation. For example, the number 4.30 x 103 contains three significant figures and the number 4.300 x 103 contains four significant figures.
      The rules for determining if a reported digit is significant are as follows: 1. Nonzero digits are always considered to be significant.
2. Zeros to the left of the first nonzero digit are never significant. 3. Zeros between nonzero digits are always significant.
4. Zeros at the right end of a number and the right of the decimal are significant. 5. Zeros at the right end of a whole number are uncertain. Whole numbers should be reported in scientific notation to clarify the significant figures.
ROUNDING NUMBERS
Since measurements always involve approximate numbers, they should be shown only with those digits that are significant plus no more than one uncertain digit. The number of digits shown is indicative of the precision of the measurement. For this reason, you should round a number by dropping one or more digits to the right. The rules for rounding are as follows:
1. If the digit dropped is greater than 5, increase the last retained digit by 1.  If the digit dropped is less than 5, do not change the last retained digit.
3. If the digit dropped is 5, increase the last retained digit if it makes it even, otherwise do not. This is called the round-even rule.
SYSTEMATIC AND RANDOM ERROR
There are two classes of errors that affect measurements: systematic errors and random errors. Systematic errors consistently appear in a measurement in the same direction. These could be caused by inaccurate calibration, mismatched impedances, response-time error, nonlinearities, equipment malfunction, environmental change, and loading effects. Systematic errors are often unknown to the observer and may arise from a source that was not considered in the measurement. Sometimes a systematic error occurs because of the misuse of an instrument outside its design range, such as when a voltmeter is used to measure a frequency beyond its specifications. (This is also called an applicational error.) Another common type of systematic error is loading error. Whenever an instrument is connected to a circuit, it becomes part of the circuit being measured and changes the circuit to some extent. Measurements in high-impedance circuits can be significantly affected if this is not taken into account. Another possible systematic error is calibration error. For example, a frequency counter uses an internal oscillator to count an unknown frequency for a specific amount of time. If this oscillator runs too slowly, then the counter waits too long, giving a result that is consistently too high. This produces a systematic error for all readings made with that counter. Other systematic errors can occur because the calibration was performed under different environmental conditions than those present when the instrument is in service. These might include temperature, humidity, atmospheric pressure, vibration, magnetic or electrostatic fields, and so forth.
    The best way to detect the presence of a systematic error is to repeat the measurement with a completely different technique using different instruments. If the two measurements agree, greater confidence can be placed in the correctness of the measurement.
    Random errors (also called accidental errors) tend to vary in both directions from the true value by chance. These errors are unpredictable and occur because of a number of factors that determine the outcome of a measurement. Random errors are generally small and may be caused by electrical noise, interference, vibration, gain variation of amplifiers, leakage currents, drift, observational error, or other environmental factors. The best way to reduce random errors is to make repeated measurements and use statistical techniques to determine the uncertainty of the final result.